A Gradient-Based Optimization Method for the Design of Layered Phononic Band-Gap Materials

作     者：Yu Huang Shutian Liu Jian Zhao 

作者机构：State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering MechanicsDalian University of Technology 

出 版 物：《Acta Mechanica Solida Sinica》 (固体力学学报（英文版）)

年 卷 期：2016年第29卷第4期

页      面：429-443页

核心收录：

学科分类：08[工学] 080501[工学-材料物理与化学] 0805[工学-材料科学与工程（可授工学、理学学位）] 

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11502043,11332004 and 11402046) the Fundamental Research Funds for the Central Universities Of China(DUT15ZD101) the 111 Project(B14013) 

主　　题：optimization band gap gradient-based optimization two-step optimization approach 

摘      要：Phononic materials with specific band-gap characteristics at desired frequency ranges are in great demand for vibration and noise isolation, elastic wave filters, and acoustic devices. The attenuation coefficient curve depicts both the frequency range of band gap and the attenuation of elastic wave, where the frequency ranges corresponding to the none-zero attenuation coefficients are band gaps. Therefore, the band-gap characteristics can be achieved through maximizing the attenuation coefficient at the corresponding frequency or within the corresponding frequency range. Because the attenuation coefficient curve is not smooth in the frequency domain, the gradient-based optimization methods cannot be directly used in the design optimization of phononic band-gap materials to achieve the maximum attenuation within the desired frequency range. To overcome this difficulty, the objective of maximizing the attenuation coefficient is transformed into maximizing its Cosine, and in this way, the objective function is smoothed and becomes differentiable. Based on this objective function, a novel gradient-based optimization approach is proposed to open the band gap at a prescribed frequency range and to further maximize the attenuation efficiency of the elastic wave at a specific frequency or within a prescribed frequency range. Numerical results demonstrate the effectiveness of the proposed gradient-based optimization method for enhancing the wave attenuation properties.